Statistical properties of defect-mediated turbulence

Abstract

Brief Reports are short papers which report on completed research which, while meeting the usual Physical Review standards of scientific quality, does not warrant a regular article (A. ddenda to papers previously published in the Physical Review by the same authors are included in Brief Reports )A. Brief Report may be no longer than 3g printed pages and must be accompanied by an abstract. The same publication schedule as for regular articles is followed, and page proofs are sent to authors We study some statistical properties of a turbulent state described by a generalized Ginzburg-Landau equation and characterized by topological defects.

Penta-Hepta Defect Chaos in a Model for Rotating Hexagonal Convection

“…Thus, in the presence of PHDs new dislocations are created through induced nucleation. As a consequence the probability distribution function for the number of defects is considerably broader than the Poisson-type distributions reported in previous studies [1,8,10]. We obtain this persistent, chaotic state in a Swift-Hohenberg-type model for rotating non-Boussinesq convection at low Prandtl numbers.…”

“…Investigators have utilized their statistical, geometrical and dynamical aspects to quantify the chaotic states in which they arise. For example, the number of dislocations (spirals) in the wave patterns governed by the complex GinzburgLandau equation has been found to obey Poisson-type statistics [10]. This suggests the interpretation that in this system dislocations are created randomly in pairs with a fixed probability, after which they diffuse throughout the system without any mutual interaction until they annihilate each other in collisions [10].…”

“…For example, the number of dislocations (spirals) in the wave patterns governed by the complex GinzburgLandau equation has been found to obey Poisson-type statistics [10]. This suggests the interpretation that in this system dislocations are created randomly in pairs with a fixed probability, after which they diffuse throughout the system without any mutual interaction until they annihilate each other in collisions [10]. The corresponding behavior and associated distribution function have also been found experimentally in electrically driven convection in nematic liquid crystals [1] and in thermally driven convection in an inclinded layer [8], and theoretically in simulations of coupled Ginzburg-Landau equations for parametrically excited standing waves [15].…”

“…Spatio-temporal chaos is at the focus of experimental [1,2,3,4,5,6,7,8,9] and of theoretical [10,11,12,13,14,15] research in high-dimensional dynamical systems. Most of the extensive studies have been devoted to variants of thermally or electrically driven convection in thin liquid layers [3,6,7,8,11,14].…”

“…In various experimental and theoretical investigations of stripe-based disordered patterns the probability distribution function for the number of defects has been used to obtain a first characterization of the defect evolution [1,8,10]. Except for the ordered chaotic state in [15], the probability distribution function for the number of defects were found to be close to a Poisson-type distribution, indicating that the dynamics are consistent with the simple diffusive model described above with very weak correlations between the defects [10]. In particular, the creation rates depend only little on the defect density [8].…”